An Economic Analysis of Black-White Disparities in

NYPD’s Stop and Frisk Program∗

Decio Coviello

hec montreal

Nicola Persico

northwestern university

May 4, 2015

Abstract

A model is introduced to explore the identification of two distinct sources of police

bias in NYPD’s “stop and frisk program:” bias at the level of the police officer making

the stop decisions, and bias at the level of the police chief allocating manpower across

precincts. Ten years of data from NYPD’s “stop and frisk program” are analyzed in

light of this theoretical framework. White pedestrians are found to be slightly less

likely than African-American pedestrians to be arrested conditional on being stopped.

We interpret this finding as evidence that the officers making the stops are on average

not biased against African Americans relative to whites, because the latter are being

stopped despite being a “less productive stop” for a police officer. We find suggestive

evidence of police bias in the frisk decision. Further research is needed.

JEL-Code: J71; K42.

Keywords: Stop and frisk, Racial Profiling.

∗Thanks to Matthew Bloch for sharing with us the NYC electoral data and to Tim Brophy for helping usin mapping the NYC data into police precincts. This paper is an update of NBER working paper #18803with the same title, published in February 2013. The data used in this paper can be downloaded from:http://www.nyc.gov/html/nypd/html/analysis and planning/stop question and frisk report.shtml. We alsooffer access to the replication material to academic faculty and graduate students. Please write to de-cio.coviello@hec.ca if you would like access.

1 Introduction

New York City’s “stop and frisk program” is a police strategy whereby pedestrians are briefly

stopped by police officers, engaged in conversation/questioning, and potentially searched.

The procedure is perceived as demeaning for those who are stopped and/or frisked. The

program also disproportionately impacts non-whites. The racial impact of the program has

given rise to public protests1 and widespread allegations of racial profiling.2 Similar programs

exist in many other jurisdictions.3

The stop and frisk program has been repeatedly challenged in court. In the most recent such

lawsuit, U.S. District Judge Shira Scheindlin said that the case involved “an issue of great

public concern,” namely “the disproportionate number of African Americans and Latinos,

as compared to whites, who become entangled in the criminal justice system.”4 The case,

Floyd et al. v. City of New York, was decided against the NYPD on August 12, 2013, with

the judge finding a violation of equal protection rights.5 The decision was front page news

on the major U.S. newspapers and gave rise to a lively public debate, with Mayor Bloomberg

accusing the judge of “deliberately denying the city a fair trial” and vowing to appeal the

decision,6 and the New York Times editorial board supporting the decision.7 This judicial

1On March 16, 2012 several thousand people marched in New York City protesting the policy, which theorganizers say “creates an atmosphere of martial law for the city’s African American and Latino residents”(see “Thousands March Silently to Protest Stop-and-Frisk Policies,” New York Times, June 17, 2012).

2According to The New York Post, “The stop-and-frisk policy has been under fire by vocal opponents,including many 2013 mayoral contenders, because the vast majority of people stopped are African Americanor Hispanic.” (Quoted from “NYPD issues department-wide memo regarding racial profiling during ’stop-and-frisks’,” May 17, 2012). Rev. Al Sharpton, writing on the Huffington Post on June 6, 2012, writes:

When a majority of those targeted by police are young men of color and when the bulk ofthem are innocent, what else are we to conclude other than the fact that the NYPD has beenimplementing a policy of racial profiling and discrimination?

3 Other major cities collect records of similar activities by their police. In Chicago police officers arerequired to file a “contact card” of every interview or pat down. These records include details of the personstopped and a description of the reason for the stop. In Los Angeles, police officers are required to completefield data reports whenever an officer stops a vehicle or a pedestrian.

4Cited from “Court Strikes Challenge to Stop-and-Frisk Trial,” Courthouse News Service, November 14,2008.

5The judge also found that the “stop and frisk” program gave rise to 4th amendment violations (unrea-sonable searches and seizures). We will not focus on 4th amendment issues.

6Quoted from “Judge Rejects New York’s Stop-and-Frisk Policy”, New York Times page A1, August 13,2013.

7See “Racial Discrimination in Stop-and-Frisk”. August 13, 2013, page A22 of the New York edition.

1

decision is likely to have repercussions on police activity, and perhaps on crime,8 in other

jurisdictions.

In this paper we examine the same “stop and frisk” data that were analyzed in the trial.

Our aim is not to “audit” the judge’s opinion from a legal perspective. Rather, we inquire

as to whether the “stop and frisk” program is administered in a racially biased way from the

perspective of social science. From this perspective, legal tests and rules of evidence are not

central; rather, what matters (or should matter) are precise definitions and the statistical

analyses that speak to them. We believe it is important for social scientists to offer their

perspective when troubling allegations of racial bias are made. We also believe that it is

important for this conversation to take place in academic journals.

In our view, the public debate on “stop and frisk” is missing a sharp definition of what

it means for the program to be racially biased. We propose one here. Following Becker

(1957), we say that a program is biased if those who administer it are motivated in part by

an (impermissible) preference for a specific racial group. Such a “distortion” in preferences

can be present at two levels: at the level of the officers making the stops; and at the level

of the police chief allocating officers to precincts. (Both levels of bias are alleged in the

public debate). In Section 2 we lay out a game-theoretic model which incorporates these

distortions, and we use it to determine which type of statistical evidence can be used to

identify bias at either level, given the presence of confounding factors (unobservables). We

conclude, consistent with previous literature, that bias at the officer’s level can be identified

by looking at the success rates of stops. We reach a negative conclusion regarding bias at

the police chief level: neither data on the frequency of stops, nor data on their success rates,

can identify a latent distortion in the police chief’s preferences. Interestingly, data on stop

frequency are not helpful for identification at either level, which is at odds with the public

focus on such data.

We then turn to the NYPD data. In Section 4 we analyze the prevalence of stops in different

racial groups and find that, by any reasonable measure, African Americans are stopped

much more frequently than whites as a proportion of their population. But, as mentioned

8 According to William Bratton, the former New York City police commissioner and Los Angeles policechief “ ... any police department in America that tries to function without some form of stop and frisk, orwhatever terminology they use, is doomed to fail.” The Associated Press, January 23, 2013.

2

above, we find it difficult to rule out unobservables, as opposed to officer bias, as potential

explanations for this disparity.

In Section 5 we turn to arrest rates and find that the arrest rates of stopped African Ameri-

cans and whites are essentially identical, at least on average across all precincts. We interpret

the latter finding as inconsistent with the hypothesis that officers are biased in their stopping

decision, at least on average.

In Section 6 we comment on the results and discuss extensions. An important extension is

to consider frisk in addition to stop decisions. Using the same methodology we find tentative

evidence suggesting police bias in the frisk decision, but further research is needed.

1.1 Related Literature

Two papers are closely related. Gelman et al. (2007) have analyzed New York City stop and

frisk data from the years 1988-89. Most of their analysis focuses on documenting disparities

in stops; using sophisticated statistical analysis they conclude that “persons of African and

Hispanic descent were stopped more frequently than whites, even after controlling for precinct

variability and race-specific estimates of crime participation.”9 In their Section 5.3 they also

briefly address the disparity in arrest rates conditional on stop, and tentatively conclude

that police officers were indeed racially biased against African Americans. This tentative

conclusion is based on the statistical fact that African Americans were less likely than whites

to be arrested conditional on being stopped. We replicate Gelman et al.’s (2007) finding in

our more recent and extensive data, but show that the finding is overturned when we add

precinct-level fixed effects. The second closely related paper is Ridgeway (2007), a RAND

report sponsored by the New York City Police Foundation. Using data for the year 2006,

this report finds that “unjustified” race disparities in stop rates are much smaller than the

ones commonly reported in the literature. Key to this finding is the choice of benchmark for

what level of disparity is “justifiable.”10 Turning to arrest rates, this report finds arrest rates

that are overall higher for whites than for African Americans (Tables 5.1, 5.2). This is the

9Gelman et al. (2007), p. 813.10Census data about the fraction of residents of a given race is deemed not appropriate. This issue is well

explained on p. 15 of the report.

3

opposite result to Gelman et al. (2007), and the same result we find in our more extensive

dataset. For this part of the analysis, Ridgeway (2007) uses a matching procedure which

re-weighs observations so as to ensure an equal distribution of several characteristics of the

stop.11 If the matching procedure uses variables that are endogenous to the outcome (racial

bias in our case), then the re-weighting procedure might not be innocuous.12

In sum, a comparison of the two papers discussed above indicates that there is no consensus

on the key question: is there any bias in NYPD’s stop and frisk program? We feel our

paper makes progress on this front. First, it organizes the evidence around a model. This

is necessary to understand what features of the data can be indicative of bias, and whose

bias (the officers’, or the chief’s) is being identified. Second, it uses a dataset which is more

recent and more comprehensive in its time span (ten years as opposed to two for Gelman et

al. 2007 and one for Ridgeway, 2007).

Knowles et al. (2001) first introduced a version of the model which we present in Appendix

A and derived Theorem 1. That paper does not feature the analysis in Section 2.2 which

is an original contribution of this paper. Also of some relevance, Knowles et al. (2001)

dealt with a setting (highway searches) which did not feature geographic units, such as the

precincts which feature prominently both in our theory and in our empirical analysis.

A more broadly related literature is that of hit rate analysis, which develops partly in reaction

to Knowles et al. (2001). See Ayres (2002), Persico and Castleman (2005), Todd (2006),

Whitney (2008), and Persico (2009) for reviews of this strategy. Ayres and Waldfogel (1994)

earlier used this strategy to look for racial bias in the judge’s decision of the level at which

to set bail. The hit rates analysis has been later utilized in the policing context by Persico

and Todd (2006), Sanga (2009), Hernandez-Murillo and Knowles (2005), Persico and Todd

11These variables include: crime suspected, precinct, average age, time of day, location, month, sex, dayof the week, type of ID (physical or verbal), whether the stop was made on a radio run, the x-y coordinatesof the stop location, being reported by witness, being part of an ongoing investigation, being in a high-crime area, being at a high-crime time of day, being close to the scene of an incident, detecting sights andsounds of criminal activity, evasiveness, association with known criminals, changing direction at the sightof an officer, carrying a suspicious object, fitting a suspect description, appearing to be casing, acting as alookout, wearing clothes consistent with those commonly used in crime, making furtive movements, acting ina manner consistent with a drug transaction or a violent crime, or having a suspicious bulge. See Ridgeway(2007), pp. 34-5

12A potential source of endogeneity might be the use of location as a matching variable. If the policeexpress their bias by over-policing a location that is mostly frequented by non-whites, the matching procedure“washes out” this channel for bias.

4

(2008), Childers (2012), Gershman (2000), Persico (2002), Persico and Todd (2005). Anwar

and Fang (2006) offer an alternative approach to hit rate analysis. Dharmapala and Ross

(2004), Alpert et al. (2005), and Smith et al. (2006) offer critical appraisals of hit rate

analysis.

2 The Model

This model is meant to conceptualize what it means for policing to be biased, and to give

guidance as to where to look for bias in the data. Agents in our model are of three kinds:

citizens of race r ∈ {A,W} living in district i, who choose whether to commit a crime which

is detected through a stop-and-frisk; a mass P of police officers who stop-and-frisk citizens;

and a police chief whose only action is to assign officers to precincts.

Following Becker (1957), we define bias as a “taste for discrimination.” By that we refer

to a component of an agent’s utility function that is dependent on the race of those with

whom the agent interacts. A key modeling choice is whether the officer’s possible taste for

discrimination is innate, or whether it reproduces the culture of the precinct to which each

officer is assigned. In this model we opt for the second possibility, and assume that officers

who are assigned to precinct i inherit the bias of that precinct.13 Therefore, in this model it

may be more appropriate to talk about precinct bias as opposed to officer bias.

The game has two stages. In the first stage, a police chief allocates police officers to precincts.

In the second stage a game within each precinct is played between officers and pedestrians.

The second-stage games (one in each precinct) are assumed to reproduce the one studied

by Knowles et al. (2001).14 Because the model is somewhat standard, we do not reproduce

its description here but we relegate it to Appendix A. The equilibrium of each precinct-

level game yields a function Kri (Pi), which summarizes for each precinct the fraction of

pedestrians of race r who commit a crime in district i when Pi officers are allocated to that

13This is done for two reasons. First, because we believe there is such a thing as a precinct culture. Second,because otherwise any observed differences in precinct bias would, within the model, result from the policechief’s choice of which officers to allocate to which district. This does not seem to us like it would be arealistic assumption given that the personnel being allocated are patrol officers, whose bias in probably notknown by the police chief.

14More precisely, in the version studied by Persico and Todd (2006).

5

district. The function Kri (P ) is derived in Appendix A.

Let us start with the first stage. What would be a “permissible” objective or motive for

the chief which defines unbiased behavior? In the case of a police chief or other central

authority allocating resources across districts, it seems reasonable to define this objective as

the minimization of crime.15 If we make this assumption, then we may conceptualize the

“legally permissible version” of the police chief’s problem as follows:

minPi

∑

i

[

NAi K

Ai (Pi) +NW

i KWi (Pi)

]

s.t.∑

i

Pi ≤ P,

where P represents the total amount of police officers available to the police chief, and N ri

denote the number of pedestrians belonging to group r. According to this formulation, the

legally permissible objective of the police chief is to minimize the sum of crimes across all

precincts.

Deviations from this behavior can be classified as biased. What would be the impermissible,

or biased, version of the police officer’s objective function? Perhaps one in which we allow the

police chief to “prioritize” the crime rate of certain precincts, which may be objectionable

especially if these priorities turn out to be correlated with the race of the precinct residents.

This can be conceptualized by assigning “welfare” weights Γi to the crime rates of precinct

i. In addition, the police chief may single out the crimes committed by pedestrians of

a particular race. We can conceptualize this by adding race-specific weights γr. Then, a

potentially biased police chief would solve the following problem:

minPi

∑

i

Γi

[

γANAi K

Ai (Pi) + γWNW

i KWi (Pi)

]

s.t.∑

i

Pi ≤ P. (1)

The parameters Γi, γA and γW in the above problem capture the police chief’s bias.

15Of note, this objective would be meaningless for the individual police officer in a district, because anindividual officer probably has a negligible impact on aggregate crime. Put differently, it would be impracticalto reward any police officer based on total crime in New York City or even in her precinct, because thatoutcome depends only minimally on the officer’s behavior.

6

2.1 Identifying Precinct-Level Bias

The precinct-level game is described and analyzed in Appendix A. The analysis reproduces

that in Persico and Todd (2006) and points to the success rate of stops as a key indicator

of officer bias. The logic, intuitively, is the following. Suppose the success rate was lower

for stops of African-American pedestrians. An officer who was not biased against African

Americans, and was motivated by the prospect of making an arrest, should cut down on less-

productive stops of African Americans and increase the more-productive stops of whites. This

“arbitrage” on the part of individual officers has aggregate effects: as officers shift to policing

whites, the crime rate in the other group rises and the crime rate among whites decreases.

This arbitrage would continue until, under a perfectly unbiased police force, arrest rates

(“hit rates”) are equalized between the stops of white and African American pedestrians in

the precinct. If the police force were biased, however, this arbitrage would stop earlier, at a

point where the differential between the African American and white arrest rates is exactly

offset by the officer’s bias. This logic gives rise to the following result, which is proved in

Appendix A.

Theorem 1 (Persico and Todd (2006): positive result on identification of police

officer bias) In the equilibrium of the precinct-level game, the arrest rate is the same across

all subgroups within a race that are distinguishable by police. Also, if the police are unbiased,

then the arrest rate is the same across races. If the police are biased against race r, the

arrest rate is lower in race r than in the other race. Thus officer bias can be identified using

arrest rates.

This theorem provides the justification for the hit rates test applied in the next section. The

theorem also identifies a significant advantage of the hit rates test: under the behavioral

assumptions stipulated in the model, the test is robust to omitted-variable bias. To see

this, interpret the subgroups mentioned in the theorem as the set of pedestrians sharing

a certain characteristic which is observed by the officer, but perhaps not observed by the

econometrician. The econometrician, therefore, only observes the average arrest rate among

all subgroups, but not the arrest rates within each subgroup. In principle this poses a prob-

lem because arrest rates within a subgroup is what identifies bias against that subgroup.

7

However, the theorem says that this is not a problem, because the equilibrium arrest rate

must the same across all subgroups within a race that are distinguishable by police, even

if these subgroups are not distinguishable by the econometrician. Therefore, the econome-

trician’s lack of ability to discern subgroups has no impact on his ability to infer bias from

arrest rates.

2.2 Identifying Bias in Manpower Allocation Across Precincts

Preliminary to the question of identifying the weights Γi, γA and γW in problem (1), a

conceptual ambiguity in the interpretation of these weights must be noted. One might be

ambivalent about whether the configuration Γi > Γj represents bias in favor or against

precinct i. On the one hand, Γi > Γj means that precinct i’s crime rate is more salient than

precinct j’s, and accordingly, more resources will be proportionally devoted to precinct i,

resulting in a lower crime rate in that precinct. On the other hand, Γi > Γj means that

precinct i will be assigned more police officers, so more stops and more frisks, which some

civil liberty advocates object to especially if police pressure correlates with the prevalence

of minorities in the neighbourhood. So, it is conceptually/normatively ambiguous whether

Γi > Γj means that precinct i is favored or disfavored relative to precinct j.

Apart from the above conceptual/normative ambiguity, there is also an empirical difficulty

in estimating the (unobserved) weights γr. To see the nature of this difficulty, let us derive

the equilibrium predictions which would allow us to estimate the weights. The first order

conditions necessary for optimality in problem (1) are:16

Γi

[

γANAi

∂

∂Pi

KAi (Pi) + γWNW

i

∂

∂Pi

KWi (Pi)

]

Pi=P ∗

i

(2)

= Γj

[

γANAj

∂

∂Pj

KAj (Pj) + γWNW

j

∂

∂Pj

KWj (Pj)

]

Pj=P ∗

j

for all i, j.

where P ∗

i and P ∗

j represent the optimal allocation. Conditions (2) represent a system of

equations, one for each precinct. In this system, N ri and P ∗

i are known. The unknowns we

16It is convenient to assume that Ci (·) is a concave function. Under this assumption, which we maintain,the first order conditions are also sufficient for optimality.

8

seek to solve for are Γi, γA and γW , which together are more than the number of equations.

Clearly, identification is not possible from this system alone. Furthermore, even if we restrict

attention to a subset of parameters (say, we somehow know the Γi’s and only need to identify

the γr’s), we can’t identify them if we do not observe the elasticities of crime to policing,∂

∂PiKA

i (Pi) . This is proved in the next theorem.

Theorem 2 (negative result on identification of police chief bias) The parame-

ter Γi cannot be identified from system (2) without knowledge of the elasticity of crime to

policing ∂∂Pi

Kri (Pi) . The parameter γr cannot be identified from system (2) without knowledge

for at least a pair (i, j) of the elasticities of crime to policing ∂∂Pi

KAi (Pi) and

∂∂Pj

KAj (Pj) .

Without knowledge of these elasticities neither crime levels (equivalent to hit rates in the

model) Kri (Pi) , nor stop intensities P ∗

i , are helpful in identifying any bias parameters in the

police chief ’s problem (1).

Proof. Let’s solve for Γ1. Write (2) for i = 1. Manipulating (2) we get

Γi

[

γANAi

∂

∂Pi

KAi (Pi) + γWNW

i

∂

∂Pi

KWi (Pi)

]

Pi=P ∗

i

= Γj

[

γANAj

∂

∂Pj

KAj (Pj) + γWNW

j

∂

∂Pj

KWj (Pj)

]

Pj=P ∗

j

.

Even if the right hand side is known, identification of Γ1 separate from the term in brackets

by which it is multiplied requires knowedge of the term in brackets. This in turn requires

knowedge of ∂∂Pi

KAi (Pi) and

∂∂Pi

KWi (Pi) . Thus the first sentence in the proposition is proved.

Now let’s solve for γA. Manipulating (2) we get

γA

[

ΓiNAi

∂

∂Pi

KAi (Pi)− ΓjN

Aj

∂

∂Pj

KAj (Pj)

]

= γW

[

ΓjNWj

∂

∂Pj

KWj (Pj)− ΓiN

Wi

∂

∂Pi

KWi (Pi)

]

.

Even if the right hand side is known, identification of γA separate from the term in brackets

by which it is multiplied requires knowedge of the term in brackets. This in turn requires

knowedge of ∂∂Pi

KAi (Pi) and

∂∂Pj

KAj (Pj) for at least one pair (i, j) . Thus the second sentence

in the proposition is proved. The third sentence follows because neither crime levels/hit rates,

nor stop intensities enter system (2) unmediated by the function ∂∂Pi

Kri (·).

9

This theorem proves an important point. Knowledge about the amount of policing directed

to precincts, or about hit rates, cannot help identify the bias parameters in the police chief’s

problem. Instead, the key statistic is an elasticity. Unfortunately, it is generally difficult to

get persuasive estimates of elasticities because elasticities captures a counterfactual: what

would happen to the crime rate if the police chief happened to perturb the allocation of

manpower from its equilibrium level. Thus, estimating elasticities requires observing more

than simply the level of crime at an equilibrium. This is an empirical challenge.17

The takeaway from this section is that identifying bias in the allocation of manpower across

precincts is difficult for two reasons. The first difficulty is of a “normative” nature, and it

has to do with what it means for an allocation to be biased against a precinct. The second

difficulty is that it is difficult to obtain empirical estimates of the weights in problem (1).

3 The Data

We use data collected by the NYPD on individual stops, questionings and frisks in the City

of New York between 2003-2012.18 This appears to be a slightly longer period than the one

at issue in the Floyd case. The database contains information on whether the person was

frisked, issued a summons or arrested, the suspect’s recorded type of crime which is recorded

as being suspected by the police making the stop, the race of the pedestrian, the timing and

location of the stop.

Unless explicitly mentioned, we restrict the sample to African-American and white pedes-

trians, setting Hispanics aside because the charge of racial bias seems to have special force

with reference to the African American population.19 In this restricted sample of 2,947,865

stops, approximately 6 percent of the stopped pedestrians were arrested and 84 percent of

the stops are of African American pedestrians, the rest of whites. Most of the suspect’s

crimes recorded by the officers making the stop fall into one of these categories: Possession

17 Typically, exogenous variation of police manpower is necessary to identify the elasticity of crime topolicing. Levitt (1997) and McCray (2001) discuss the difficulties of estimating such elasticity.

18The database can be downloaded at the following link:http://www.nyc.gov/html/nypd/html/analysis and planning/19We briefly extend our focus to Hispanics in Section 6.2.

10

of a Weapon (27%); Robbery (17%); Criminal Trespass (12%); Grand Larceny Auto (9.1%);

Burglary (8.9%).20 Table 1 reports some descriptive statistics.

A possible caveat regarding these data is that NYPD officers are not required to record

all interactions with private citizens.While NYPD policy requires officers to fill out a UF-

250 form for every Terry stop,21 NYPD policy also specifically enumerates the circumstances

requiring the completion of form UF-250. The specific circumstances are: a person is stopped

by use of force; a person stopped is frisked or searched; a person is arrested, or a person

stopped refused to identify himself (and was later identified by the officer).22 It is possible,

therefore, that recorded stops (the ones in our database) may be a selected sample of all

stops. Judge Schendlin notes the data limitations, but ultimately accepts the data as a

useful, albeit imperfect, tool to aid her decision. We do the same in the main body of the

paper.

It is tempting to address the selective recording concern by restricting the sample to stops

that are required by law to be recorded. Within this sample, the problem of selective

recording should not exist. The trouble with this strategy is that, at the time of choosing

whom to stop, the officer cannot distinguish whether the stop will develop into one that

has to be recorded or not. Conditioning our analysis on such ex-post information would

mean conditioning on information not possessed by the officer at the time of the stop. Put

differently, the outcomes contained in this restricted data set cannot be said to fully portray

the outcomes generated by any officer’s stop behavior. Thus, the hit rate analysis cannot

properly be applied to such a subsample. Nevertheless, for completeness in Appendix C

we construct a sample which we believe approximates the “mandated reports” subsample,

and we replicate our analysis on that sample. That analysis identifies bias against African

Americans.

A second, very important caveat must be raised regarding the suitability of arrests as an

20Other crimes are: Grand Larceny (4.3%); Illegal Possession of Substances (3.6%); Marihuana (3.3%);Assault (4%); Illegal Sales of Substances (2.9%); Petit Larceny (2.5%); Mischief (1.2%); Graffiti (1.1%).

21 From the patrol guide 212-11.6: “Prepare STOP, QUESTION AND FRISK REPORT WORKSHEET(PD344-151A) for EACH person stopped” (emphasis theirs).

22 See pg. XV of the New York Attorney General report on Stop and Frisk. The report is downloadablehere:http://www.oag.state.ny.us/sites/default/files/pdfs/bureaus/civil rights/stp frsk.pdf The outcome “refusedto identify” is not recorded in the data. We proxy for it using the field “evasive response to questioning.”

11

Table 1: Descriptive Statistics

Mean sd nOutcomesArrest made 5.8 23 2,947,865Race of the pedestrianAfrican American 84 37 2,947,865Suspect’s recorded type of crimePossession of a Weapon 27 44 2,496,267Robbery 17 37 2,496,267Criminal Trespass 12 32 2,496,267Grand Larceny Auto 9.1 29 2,496,267Burglary 8.9 28 2,496,267Grand Larceny 4.3 20 2,496,267Illegal Possession of Substances 3.6 19 2,496,267Assault 4 20 2,496,267Marihuana 3.3 18 2,496,267Illegal Sales of Substances 2.9 17 2,496,267Petit Larceny 2.5 16 2,496,267Mischief 1.2 11 2,496,267Graffiti 1.1 10 2,496,267Other Crimes 4.3 20 2,496,267

Notes. Variables expressed in percent. African Americanis an indicator variable coding the pedestrian’s race. Crimedetails are 13 indicators of the suspect’s recorded type ofcrime represent 95% of the crimes recorded in the sample.Years 2003-2005 have missing values in the variable Crimedetails.Source. Statistics for the City of New York, Years 2003-2012.

outcome for hit rates analysis. The ideal outcome is a measure of productivity which the

officer legitimately maximizes, and which is itself “objective,” that is, is not tainted by police

bias. Arrests might not be “objective” because they might be subject to police discretion,

and thus may themselves be tainted by police bias. For example, all else equal, the police may

be more likely to arrest an African-American than a white pedestrian after having stopped

either. This is a very valid concern. The best evidence to address this concern would be the

rates at which arrests, which are usually warrantless in our sample, are later upheld by a

judge.23 Unfortunately, such data are not available to us. We return to this issue in Section

6.4.

23Because the conversion is done by a judge, it is arguably an “objective” outcome, in the sense that anyjudicial bias should be uncorrelated with the bias of the police officer making the arrest.

12

4 Disparities in Police Pressure

New York City’s stop-and-frisk program disproportionally impacts minorities. The New York

Civil Liberties Union makes this point forcefully by documenting that, in 2011, 52.9 percent

of stops were of African Americans, 33.7 percent were of Latinos, while whites accounted

for only 9.3 percent of the stops.24 After restricting attention to African Americans and

whites only, the following figure 1 (left panel) summarizes this striking disparity.25 The

panel depicts the difference in police pressure by race of the pedestrian. For each race, police

pressure is defined as: average number of stops in a year divided by total population in NYC.

In the whole sample, pressure is about ten times larger for African Americans as it is for

whites.

This disparate impact is certainly problematic from a social viewpoint. However, disparate

impact can reflect many factors, both observable and unobservable, which affect the stop-

and-frisk process. Neither Theorem 1 nor Theorem 2 indicate that police pressure can help

identify police bias. This lack of theoretical framework becomes problematic when, as in

Table 2, conditioning on observables attenuates the disparity. Let us turn to this table.

Table 2 makes use of variability across precincts. The dependent variable is the ratio of

African American/white police pressure.26 Column (1) shows that this disparity in police

pressure is correlated with the precinct’s racial makeup. From an a-theoretical perspective

this dependence on race seems troubling. However, columns (2) and (3) show that condi-

tioning on income takes away the effect of race (and in addition eliminates the significance

of the constant in the regression).27 Thus, it now appears that police manpower is being al-

located disproportionally to precinct with poorer residents – which is arguably less bad than

allocating disproportionally to minority precincts. Is this encouraging news? Does this say

anything about police bias? In our view, it is difficult to learn much from this a-theoretical

24See NYCLU (2011), pg.5.25The figure reports the yearly average number of stops over resident population (left panel) and the

yearly average arrests over yearly average stops (right panel) divided by ethnicity in New York City (in %).Statistics for the City of New York, Years 2003-2012. Resident population from the 2010 Census data.

26The table shows that, averaging within precincts first, then taking arithmetic average of precinct-levelmeans, the ratio of African American/white police pressure is 17. This figure differs from the ratio (about10) implied by Figure 1, left panel, because in that figure the average was computed at the city-wide level.

27All variables included in this regression are described in Appendix D.

13

Figure 1: Police Pressure and Hit Rates in New York City

1.3

11.8

05

1015

Perc

ent

White African American

Stops Over Resident Population (by Race)Police Pressure:

6.1

5.7

02

46

Perc

ent

White African American

Arrests Over Stops (by Race)Hit Rates:

approach except at a descriptive level. For this reason we regard the estimates in this sec-

tion as suggestive, but not dispositive, about the presence of bias. We turn, therefore, to

the analysis of arrest rates which has its theoretical underpinning in Theorem 1.

14

Table 2: Correlates of Relative Police Pressure in New York City

Model OLS OLS OLSSample Panel Panel Panel

(1) (2) (3)Fraction of African American -0.222*** -0.057 -0.066

(0.073) (0.055) (0.049)Income 0.365*** 0.307***

(0.119) (0.115)Constant 23.118*** -2.910 -10.874

(3.857) (6.473) (24.535)

Relative police pressure (average) 17Fraction of African Americans (in %) in the average precinct 26.78Number of precincts 75 75 75Observations 750 750 750Adj. R2 0.083 0.266 0.467Precinct Controls no no yesTime FE no yes yes

Notes. Estimates are on 75 precincts. The dependent variable is (relative) police pressure

(ArrestsofAfricanAmericansAfricanAmericanpopulation

ArrestsofWhitesWhitepopulation

) in New York City. Fraction of African American is the percentage of

the population that is African American in the precinct in 2010. Income is the inflation adjustedmedian income in the precinct in 2010. Column 3 also includes the difference between M. Bloombergand the first running opponent M. Green, or F. Ferrer, or B. Thompson vote share in the 2001, 2005,2009 elections, respectively. Missing years are computed using moving averages; the percentage ofthe population that is African American in the precinct in 2010; the inflation adjusted median in-come, 2010 precinct average; the median age, 2010 precinct average; the precinct average percentageof the population that is female in 2010; the precinct average percentage of the population aged15-24 with a college degree in 2010; the number of annual crimes (murders, rapes, robberies, fel.assaults, burglaries, grand larcenies, grand larceny autos) in each precinct divided by the precinctpopulation in 2010 (in 1,000 habitants) for the years 1998, 2001, 2012; the number of annual graf-fiti in each precinct in 2011 divided by the precinct population in 2010 (in 1,000 habitants); thetotal number of annual civic initiatives (education, emergency preparedness, environment, helpingneighbours in need, strengthening communities) in each precinct, in 2011 divided by the precinctpopulation in 2010 (in 1,000 habitants); and an indicator for African American commanding officers.All variables are described in Appendix D.To control for possible time trend in the dependent variable and precincts specific characteristics,when denoted with “yes” regressions additionally include year fixed effects (9 dummies). Standarderrors are clustered at the precinct level. Significance at the 10% (*), at the 5% (**), and at the 1%(***).Source. Statistics for the City of New York, Years 2003-2012. Resident population from the 2010Census data.

15

5 Analysis of Arrest Rates

Theorem 1 indicates that a comparison of arrest rates by race can identify bias in the police

officers’ stop decision. In this section we compute arrest rates and compare them across

races.

We start by noting that, in the aggregate, the probability that a stop translates into an

arrest is quite similar across races in our sample. This is shown by regressing an indicator

variable coding whether the stopped pedestrian was arrested on another indicator variable

coding the pedestrian’s race. Figure 1 (right panel) shows the aggregate arrest rates for

stopped pedestrian of either race. Clearly, the large disparity across races that is present in

police pressure (left panel) is absent when we look at average arrest rates.

More detailed estimates are reported in Table 3. Depending on the specification, African

American pedestrians who are stopped are between 0.42% and 0.44% less likely to be arrested

compared to whites (columns 1-3). Thus the probability of a stop resulting in an arrest is

about 6% for whites v. 5.6% for African Americans. Although the difference is very small,

and perhaps unlikely to be perceived by an officer based on his own experience alone, the

difference is significant in two out of three specifications. This pattern is similar to that

found by Gelman et al. (2007) in their more limited sample.

This small difference in arrest rate between races changes sign, however, when we control

for precincts. Precincts vary considerably in the likelihood that a stop translates into an

arrest (refer to Figure 2).28,29 Controlling for precincts is appropriate because precints are, in

effect, separate jurisdictions.30 Controlling is also necessary to avoid fallacy in aggregation,

if baseline arrest rates are correlated with race.

To understand the possible fallacy let’s, for the sake of argument, treat precincts as separate

jurisdictions. If the police officers in each precinct were unbiased, then within each precinct

28The figure reports the probability of being arrested conditional on being stopped in New York City (in%). Statistics for the City of New York, Years 2003-2012.

29This is not surprising, given the heterogeneity among precincts. For institutional information aboutprecincts, refer to Fyfe and Kane (2006).

30The NYPD is organized in 76 precincts, each of which is responsible for a specific geographic area. Anofficer from one precinct cannot stop pedestrians in another precinct. According to the New York stateCriminal Procedure Law (CPL.140.50) , “a police officer may stop a person in a public place located withinthe geographical area of such officer’s employment”.

16

Table 3: Arrest Made

Model OLS OLS OLS FE FE FE FE(1) (2) (3) (4) (5) (6) (7)

African American -0.420*** -0.437*** -0.437 0.379*** 0.355*** 0.355* 0.340*(0.037) (0.037) (0.469) (0.046) (0.046) (0.207) (0.204)

Constant 6.140***(0.034)

Mean outcome 5.79%Fraction of African American 84%P-value of H0 : ui = 0 0.001 0.001 0.001 0.001Number of precincts 76 76 76 76Observations 2,947,865 2,947,865 2,947,865 2,947,865 2,947,865 2,947,865 2,947,865Cluster SE no no yes no no yes yesTime FE no yes yes no yes yes yesPrecincts FE no no no yes yes yes yesTime FE · Precincts FE no no no no no no yes

Notes. Estimates are on 76 precincts. The dependent variable is the probability of being arrested conditional on beingstopped in New York City (in %). African American is an indicator variable coding the pedestrian’s race. To control forpossible time trend in the dependent variable and precincts specific characteristics, when denoted with “yes”, regressionsadditionally include year fixed effects (9 dummies) and precincts fixed effects (75 dummies). In Column 7, we includeinteractions between year fixed effects (9 dummies) and precincts fixed effects (75 dummies). Columns 3, 5-7, shows showclustered standard errors at the precinct level. P-value of H0 : ui = 0 is the p-value for the joint test of all the precinctsfixed effects equal to zero. Significance at the 10% (*), at the 5% (**), and at the 1% (***).Source. Statistics for the City of New York, Years 2003-2012.

the arrest rates of African American and white pedestrians should be the same conditional

on being stopped. However, the levels of these arrest rates need not all be the same across

precincts. For example, suppose hypothetically that of all the African Americans and whites

stopped in the Bronx 3% were arrested, and 6% of the African Americans and whites stopped

in the Financial District were arrested. If we aggregated the data from the two precincts

we would mistakenly conclude that the police officers making the stops are biased against

African Americans, because in the aggregate sample most African Americans are searched

in the Bronx and have a 3% arrest rate, much lower than whites, most of whom are searched

in the Financial District. Thus the hit rate test carried out without controlling for precincts

would be potentially biased, or more precisely, uninformative about the racial bias exhibited

by police officers within each precinct.

A solution to this aggregation problem is to introduce precinct-level fixed effects in the

statistical model that predicts arrest rates. In the above hypothetical example, introducing

precinct-level fixed effects into the baseline specification allows the fixed effects to absorb

the 3% and 6% baseline arrest rates, while the coefficient on “African American ” would

17

be estimated to equal zero. This zero coefficient would properly be interpreted as evidence

that the police are not biased. Conversely, if the police were biased then we would observe

lower arrest rates on African American searchees in many or all precincts, and this African

American-white difference in arrest rates would be picked up by the coefficient on “African

American,”after controlling for precinct-level fixed effects. Therefore, controlling for precinct

fixed effects is necessary for the hit rates test to function properly. Hence, precinct-level fixed

effects regressions represent the paper’s preferred specifications.

Figure 2: Probability of Being Arrested Conditional on Being Stoppedin New York City

7.93 − 13.026.22 − 7.935.15 − 6.222.37 − 5.15

In columns 4-7 of Table 3 we run the same OLS regressions, this time with 76 precincts-level

fixed effects. Notably, the coefficient on “African American” changes sign. Now, stopping

an African-American pedestrian results in a probability of arrest which is larger by 0.355%

compared to a white pedestrian. That is, after accounting for the fact that different precincts

have different “baseline” rates of arrest conditional on search, African Americans are no

18

longer less likely to be arrested conditional on being stopped.31 Based on Theorem 1, this

evidence is interpreted as rejecting the hypothesis of a relative bias against African Americans

in the officers’ stop decisions, at least on average across precincts. This is a key message from

our analysis.32 The evidence so far is consistent with the interpretation that, on average,

there is no bias against African Americans in the police officers’ stop decisions.

It is important to point out that our main result is obtained without controlling for the “sus-

pected crime”characteristic that is reported by the police officer. This is because Theorem

1 only requires equalization across dimensions that are visible before the stop, and hence

can be used by the police to choose whom to stop. In contrast, the information contained

in the “suspected crime” variable appears to reflect knowledge that can most plausibly be

acquired during the stop. (For instance, among the “suspect’s recorded crime” categories

we find “criminal possession of controlled substances,” “of marihuana,” “of a weapon.”) If

post-stop information is included in the regression and this information is correlated with

race, then the hit rates test might be invalidated. To see this imagine, hypothetically, that

most African Americans who are stopped end up being arrested for substance possession, but

whites who are stopped end up being arrested for all sorts of crimes. In this case introducing

the variable “substance possession” (which is post-stop information) in the regression might

soak up a lot of the predictive power which would otherwise accrue to the dummy “African

American” and, therefore, potentially reduce the absolute magnitude of the estimated co-

efficient on the dummy. So, if the police were actually biased the estimated coefficient on

the “African American” dummy would not capture the full extent of police bias due to the

presence of the inappropriate control for “suspected crime.” In any case, putting aside this

theoretical argument, in Section 6.4 we repeat our analysis controlling for “suspected crime”

and establish that our finding persists in that specification.

31The precinct-level fixed effects jointly explain, in a statistical sense, the arrest rate (i.e., the p-value isless than 5% for the joint test of all the precincts fixed effects equal to zero, see Table 3).

32For completeness, we repeat the analysis on the subsample of stops that are required by law to bereported, see footnote 22. In this subsample the coefficient on “African Americans” does not become positivein the specification with precinct-level fixed effects. However, the estimates obtained controlling for thesuspect’s recorded type of crime, and the police pressure analysis are invariant to this sample selection. Asmentioned before, this subsample cannot be a proper sample for a hit rate analysis. Therefore, we disregardthe results from this analysis.

19

6 Discussion and Extensions

6.1 A Tale of Two Measures

Most of the public debate considers the wide racial disparity in police pressure (see Figure

1, left-hand panel) as a strong clue, if not outright evidence, that the police act in a racially

biased way. Our theoretical analysis (Theorems 1 and 2) has led us to conclude that bias, to

the extent that it can be identified with the data at hand, ought to be inferred from disparities

in arrest rates (see Figure 1, right-hand panel). One might ask whether these two measures,

police pressure and arrest rates, are correlated across precincts. In other words, if we take

arrest rates differential as a good proxy of bias, are these differentials related to differentials

in police pressure? Figure 3 below suggests that this is not the case in our sample.33 The

horizontal axis reports the ratio, computed at the precinct level, of the two columns in Figure

1, left panel. This is a measure of how much higher police pressure is on African American

citizens, compared to whites. The vertical axis represents our measure of bias (difference

between African American and white arrest rates, 10-year average, by precinct). The figure

suggests that there is no correlation between these two measures across precincts.34 We

interpret this observation as going against the presumption that large disparities in police

pressure are necessarily correlates of police officer bias.

6.2 Hispanics

So far we have restricted the hit rate analysis to African-American and white pedestrians,

setting Hispanics aside. We now extend our analysis to a sample of 4,413,566 stops and

frisks of African Americans, Hispanics (black and white) and whites suspects. In this larger

33The figure plots the differential probability of an African American being arrested (i.e., the estimatedcoefficient in the univariate regression of arrests on an indicator variable for african-american pedestrians)

against the natural logarithm of relative police pressure:ArrestsofAfricanAmericansAfricanAmericanpopulation

ArrestsofWhitesWhitepopulation

in each of the New York

City police precinct.Source. Statistics for the City of New York, Years 2003-2012.34 This graphical intuition is supported by a regression analysis showing that relative police pressure is

uncorrelated with our measure of bias. Results of these regressions are not reported and are available onrequest.

20

Figure 3: Differential Probability of an African American being Ar-rested and Relative Police Pressure

1

5

6

7

9

10

131417

18

19

20

23

24

2526

28

30

3233

34

4041

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44

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46

47

4849

50

52

60

6162

63

66

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69

70

7172

73

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76 77 7879

81

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84

8890

94

100

101102103

104105 106

107 108 109

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114115

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123

−1

0−

50

5D

iffe

ren

tial P

rob

. o

f a

n A

fric

an

Am

erica

n b

ein

g A

rre

ste

d (

in %

)

0 1 2 3 4 5Relative Police Pressure (in logs, for readability)

sample, African Americans and Hispanics represent 56.1 % and 33.2 % of the stops, and

suspects are arrested, on average, 6 % of the times.

In Table B.1 we augment our baseline specification regressing the indicator variable coding

whether the stopped pedestrian was arrested on an indicator variable for African-American

pedestrians and on an indicator for Hispanic pedestrians. Depending on the specification,

Hispanic pedestrians who are stopped are between 0.12% and 0.15% less likely to be arrested

compared to whites. This small difference in arrest rate between races, however, vanishes if

we control for precincts fixed effects.35

35In Table B.2 we control for the suspect’s recorded type of crimes and find similar results.

21

6.3 Other Characteristics

So far we have focused on race and ethnicity. Other characteristics of the stop are available

in our data such as gender, time of the stop, etc. To the extent that these are known to

the officer before the stop, the theory predicts that the return to these searches should be

similar provided that the search cost is similar across characteristics. In Table 4 we compare

arrest rates across these characteristics.

Although arrest rates are not equalized across characteristics they are generally close, in

the sense that for most characteristics the estimates of the differential probability of being

arrested are within 1%. Our favored interpretation for these coefficients is that such small

statistical differences would be difficult for police officers to detect based on their individual

experience. Moreover, the signs of some of the estimated coefficients might be compatible

with the theoretical predictions discussed in Section 2.36 For example, the negative coefficient

(-.94%) for “Stop between 7pm-6am ” would arise in equilibrium if an arrest for a night crime

is perceived by the officer as “more valuable” than an arrest for a day crime (perhaps because

the law tends to treat night crimes more severely).

The exceptions are the coefficients for women (+2.3%) and heavily built pedestrians (+1.2%);

these higher arrest rates are indicative, in our framework, of a relative reluctance by officers

to stop and frisk these categories. Why might officers refrain from stopping and frisking

heavily built pedestrians and women? (Currently, only 7.4% of all stops are of women).

We conjecture that (mostly male) officers might shy away, at the margin, from searching

women because such stops, though lawful, are even more controversial than those of male

suspects.37 However, an analysis of this gender disparity is deferred to future work. The

inferred reluctance to stop and frisk heavily-built men may be due to a possibly higher risk

of an aggressive reaction.

It is worth noting that conditioning on all these characteristics does not affect the main

estimate of interest in this paper. Columns 1 and 2 in Table 4 indicate that even after

36 We thank the editor for pointing out this observation.37See “For Women in Street Stops, Deeper Humiliation,” by Wendy Ruderman. The New York Times,

published August 6, 2012. The article indicates that in 2011 more than 80% of patrol officers were men,and that it is deemed unsafe and often impractical for male officers to summon a female officer in order toconduct a frisk of a female pedestrian.

22

controlling for these characteristics, the estimated coefficients on the African Americans

indicator are parallel to those in Table 3.38

Table 4: Other Pedestrians CharacteristicsSample All African American WhiteModel OLS FE OLS FE OLS FE

(1) (2) (3) (4) (5) (6) )African American -0.367 0.423**

(0.469) (0.202)Female 2.317*** 2.308*** 2.737*** 2.729*** 0.838*** 0.759***

(0.293) (0.260) (0.366) (0.323) (0.295) (0.266)Above 6 feet 0.553*** 0.434*** 0.477*** 0.354*** 1.095*** 0.966***

(0.068) (0.047) (0.070) (0.052) (0.187) (0.153)Heavy build 1.224*** 1.121*** 1.176*** 1.053*** 1.420*** 1.412***

(0.116) (0.112) (0.116) (0.114) (0.238) (0.207)Above 18-yrs 0.733*** 0.469*** 0.605*** 0.386** 1.548*** 0.938***

(0.176) (0.150) (0.202) (0.177) (0.285) (0.167)Stop between 7pm-6am -0.981*** -0.939*** -1.160*** -1.104*** -0.030 0.012

(0.152) (0.160) (0.167) (0.178) (0.264) (0.239)Constant 5.289*** 6.367*** 7.640*** 9.651*** 4.826*** 3.649***

(0.474) (0.339) (0.689) (0.479) (0.533) (0.595)Prob. of Arrest 5.855 5.786 6.217Fraction of African American 0.840 1 0Fraction of Female 0.0741 0.0687 0.102Fraction of Above 6 feet 0.614 0.618 0.593Fraction of Heavy build 0.0878 0.0897 0.0775Fraction of Above 18-yrs 0.847 0.843 0.868Fraction of Stop between 7pm-6am 0.459 0.460 0.451Observations 2,853,320 2,853,320 2,397,038 2,397,038 456,282 456,282

Notes. Estimates are on 76 precincts. The dependent variable is the probability of being arrested conditional on being stoppedin New York City (in %). African American is an indicator variable coding the pedestrian’s race; Female is an indicator variablecoding the pedestrian’s gender; Above 6 feet is an indicator variable for pedestrians above 6 feet height; Heavy build is an indicatorvariable for heavy build pedestrians; Above 18-yrs is an indicator variable coding whether the pedestrian is 18 years old or morerace; Stop between 7pm-6am is an indicator variable for night stops. To control for possible time trend in the dependent variableand precincts specific characteristics regressions additionally include year fixed effects (9 dummies); even columns include precinctsfixed effects (75 dummies). P-value of H0 : ui = 0 is the p-value for the joint test of all the precincts fixed effects equal to zero.Cluster adjusted at precinct level standard error are reported in parenthesis. Significance at the 10% (*), at the 5% (**), and atthe 1% (***).

Source. Statistics for the City of New York, Years 2003-2012.

38The estimates of Table 4 differ slightly from those of Table 3 because of the smaller sample in the lattertable, which is due to missing values in pedestrians characteristics.

23

6.4 Arrests As an Outcome For Hit Rates Analysis

In this section we explore the concern raised at the end of Section 3, that arrests might not

be an objective outcome. To assess the objectivity of arrests, ideally, one would want data

on the fraction of arrests resulting from stops that are dismissed either by prosecutors before

they get to court or by judges at a later proceeding. Unfortunately we do not have access

to such data.

We follow an (admittedly imperfect) alternative strategy by looking at the officer’s behavior

after the stop has been made. We check whether, given the suspect’s type of crime as recorded

by the police officer after the stop, the officer is more likely to arrest a African American

than a white pedestrian. To see why this exercise speaks to the issue, imagine that out of

100 stopped African Americans the police identifies 2 with weapons which it suspects (or

believes) may be illegally held. Out of 100 stopped whites, the police identifies 4 with such

weapons. If the police arrests all blacks with such weapons but only half of the whites with

such weapons, then our test of bias in the decision to stop will indicate equal success rate

of stops (2% in both races) and will therefore absolve the police of bias in the stop decision.

However, in this example African American suspects are actually being arrested more often

than whites for the same suspect’s type of crime (as recorded by the officer), which indicates

bias in the arrest decision.

To check for bias in the arrest decision, we check whether the race of the person stopped pre-

dicts the probability of arrest after conditioning on the suspect’s recorded crime (as recorded

by the officer on Form UF-250). This test will reveal whether the police shows a race-based

disparity in translating a suspect’s crime into arrest. An implicit assumption behind this

test is that there is no discretion in the officer’s recording of the suspect’s crime. Note that

this is a test of bias in the decision to arrest, and is therefore distinct from the main test in

the paper which looks for bias in the stop decision.

Table B.3, in Appendix B, presents the results. When we control for type crime African

Americans are slightly more likely to be arrested 0.225% but the effect is not statistically

significant. We interpret this result as consistent with the hypothesis that, given a suspect’s

crime (as recorded by the officer) of a pedestrian of either race, officers are not using discretion

in deciding whom to arrest, or at least, that any discretion they use is uncorrelated with

24

race. Therefore, we do not find evidence against using the outcome “arrest” as the outcome

in the hit rate test.

We also break down the reasons for arrest by race of the pedestrian, to explore whether

some “reasons” might be more manipulable by biased officers. Table B.4 reports the ev-

idence. Unfortunately, we do not feel that there is a clear ranking of “reasons” in terms

of manipulability. In the end, we believe that the objectivity of the arrest decision is an

assumption that cannot be fully tested in the data publicly released by the NYPD.

6.5 Alternative Unit of Analysis: Frisks

Until now the analysis has focused on bias in the stop decision, ignoring whatever transpires

between a stop and an arrest. In this section we focus on frisks. About 53.7% of stops of

African Americans develop into frisks, as opposed to 39.3% of whites. Thus, stops of African

American pedestrians are more likely to develop into a frisk. Frisks of African-American

pedestrians are also less likely to be “productive,” compared to frisks of Whites: about 9%

of frisks of African Americans are associated with an arrest, compared with 13% of Whites.

This disparity in arrest rates is suggestive of bias in the frisk decision. In a previous version of

the paper, available on request, we lay out a heuristic dynamic choice model where the officer

must first decide whom to stop (a stop costs the officer t1) and then, with the additional

information that becomes available after the stop, whether to frisk (at an additional cost

t2).39 We derive a modified hit rates test for that model. When applied to our data, the

test indicates that the 9-to-13 percent disparity is inconsistent with the null of no bias ift2t1

> 34, that is, if the additional cost of a frisk is large relative to the cost of a stop. The

intuition for this result is as follows. The officer will arbitrage across frisks (do I frisk the

39The heuristic model is as follows. The police officer first decides whether to expend cost t1 and stop apedestrian. Then, after having interviewed the pedestrian and learned some unobserved (to us) characteristicu, the officer will be able to immediately make an arrest, or may choose to frisk the pedestrian at an additionalcost t2, or may choose to let the pedestrian go. In this model, the officer uses knowledge of u, which is gainedafter the stop, in his decision of whether to frisk. Only those pedestrians with u’s suggesting a sufficientlyhigh likelihood of a crime will be frisked. Note that in the equilibrium of this model it is possible to havetwo characteristics u1 and u2, both of which lead to a frisk, but with u2 yielding a slightly higher probabilityof a successful frisk. Such small differences in the returns to frisk are not be arbitraged away in equilibriumbecause officers need to pay t1 in order to learn whether a pedestrian has characteristic u1 or u2. The modelyields precise bounds on the disparity in hit rates which can still be compatible with no bias, for each givenratio t1/t2.

25

pedestrian I have stopped already, or do I pass and possibly frisk the next pedestrian I stop?)

in the same way that, in our main model, he arbitrages across stops. However, note that

arbitraging across frisks (that is, opting to frisk the next pedestrian you stop as opposed to

the one already stopped) requires paying an additional “stop cost” t1. If t1 is large arbitrage

will be limited. Conversely, if the stop cost t1 is small we should expect arbitrage to work

powerfully to equate the difference in success rates across races.

Some further insight can be obtained if we condition on a specific crime suspected, such

as weapons possession, for which we think that (1) a frisk is always warranted (indeed,

the justification for the doctrine of the Terry stop is for the police to check a suspect for

weapons) and (2) a frisk will generate objective evidence either inculpating or exculpating

the pedestrian. About one in four (27%) of all stops are associated with “suspected weapons

possession;” of these, 93.5% are of African-Americans (see Appendix B, Table B.5). If the

police claim that they suspected weapons possession, then a large disparity in frisk rates

among those stops favoring whites might be prima facie evidence of racial bias. Likewise,

looking only at stops involving suspicion of weapons possession and a frisk, differences in

arrest rates could be interpreted through the lens of a hit-rate test.

Table B.5 shows that, in the subsample of those who are suspected of carrying a weapon,

whites are frisked 82.4% of the times and African Americans are frisked 85.7% of the times.

This statistically significant difference (about 3%) suggests, but does not establish, that

blacks are somewhat over-frisked compared to whites. Let’s look at the “success rates” of

these frisks. There are two natural definitions of success for such a frisk: that the pedestrian

is arrested for illegal weapons possession, or that the pedestrian is arrested for any reason.

Regardless of how success is defined, in our subsample frisks of African Americans are less

likely to be successful compared to frisks of Whites. Table B.6 shows that, in the subsample

of those who are suspected of carrying a weapon and have been frisked, Whites are arrested

for weapons possession 2.6% of the times and African Americans are arrested 1.2% less often.

This difference is statistically significant. Turning now to arrests for any reason, Table B.7

indicates that Whites are arrested 6.7% of the times and African Americans are arrested

2.3% less often. This difference is also statistically significant.

Overall, these disparities in success rates suggest officer bias in the frisk decision. This

26

conclusion is subject to the caveat mentioned before: that the arbitrage across frisks here is

potentially costly because it requires the officer to incur a number of stops (about four, in

our data) before finding another pedestrian who, after being stopped, becomes suspected of

weapons possession. To the extent that this arbitrage is costly, small disparities in success

rate may not be indicative of bias. Further research is required on the question of bias in

frisk behavior.

6.6 Alternative Outcome: Summons

Summonses represent notices of violation issued by police officers during the stop of a suspect.

These notices often entail an order to appear in court. In our sample, 6 percent of the

stopped pedestrians were issued a summons and 84% of the summonses were issued to

African Americans. Most of the summonses in our data fall into one of these categories:

Disorderly Conduct, Opening of a Container, Trespass, and Consumption of Alcohol on

Street.

Presumably, issuing a summons is a lesser or secondary goal for a police officer compared to

an arrest. Nevertheless, issuing a summons does make the stop to some extent successful, or

productive. Therefore, in Appendix B, Table B.8 we perform the hit rate test on the outcome

“summons issued.” The results are the opposite of Table 3: after controlling for precincts, the

sign on “African American” switches and becomes negative.40 The interpretation, according

to the hit rate analysis, would be that officers are biased against African Americans in their

decision to stop if officers only cared about issuing a summons. But, probably it is proper

for officers to care both about issuing a summons and about making an arrest.

This reasoning leads us to add a dimension to the model: the rate at which police officers

trade off arrests and summons. Mathematically, the officer’s payoff from a stop can be

40Table B.9 in Appendix B corresponds to Table B.3 and gives a similar result: given a certain crimecommitted by a pedestrian of either race, officers are not using discretion in favor of whites when decidingwhom to issue a summons to. In fact, African Americans appear to be issued summons less often than whites.Therefore, we see no evidence of police discretion that simultaneously affects the outcomes “summons” andis biased against African Americans.

27

conceptualized as follows:

π (α) = α · Iarrest + (1− α) · Isummons,

where Iarrest and Isummons are indicators taking value 1 if the pedestrian is arrested or issued

a summons, respectively. If α is close to zero then the payoff π (α) will closely mimic the

variable “summons;” and vice versa, when α is close to one then the payoff π (α) will be

close to the variable “arrests.”

Once the model is extended in this way, there are two unobserved parameters in the officer’s

objective function: one is the officer’s possible bias against African Americans; the other is

the parameter α. For the purpose of this paper, both parameters are taken to reflect the

police officer’s tastes or values.41 Both parameters, arguably, have a normatively correct

value: for bias this value is obviously zero, that is, no bias; we do not take a stand on the

normatively correct value of α, instead we will carry around this value as a free parameter

α∗. If the parameters in the officer’s utility function differs from their “normatively correct”

values, then the officer’s behavior will lead to a disparity in hit rates, where the hit rates are

computed on the variable π (α∗). But it will be difficult to determine whether the disparity

is due to racial bias or to a normatively incorrect α (or both). Given this ambiguity, in

the rest of the section we perform the following analysis. We stipulate as part of our null

hypothesis that the police are unbiased, which implies that in equilibrium the hit rates on

African American and whites need to be equalized on the variable π (α), whatever α is in the

officer’s mind (this prediction comes from the reasoning in Section 2). We then we look for

the value α which equalizes the hit rates on the variable π (α) . The resulting α is interpreted

as the taste parameter which, given the null of no bias, rationalizes the officers’ observed stop

behavior. After this exercise, which is purely an exercise in the identification of unobserved

taste parameters, we go back and ask the question of whether the estimated parameter α

is normatively acceptable. If it is not, then we conclude that the police are behaving in a

way that departs from the norm—even though we will not be able to distinguish whether

the departure is that the officer is racially biased, or that the officer’s α differs from the

normatively acceptable α∗, or both.

41In a broader treatment, one could argue that α might be determined by career incentives, for example.

28

Let’s proceed. Fix any α which we interpret as the known taste parameter in the police

utility function. What happens if we run the hit rate test on the outcome variable π (α)?

This depends on the chosen value of α. If α is close to zero then the payoff π (α) will closely

mimic the variable “summons,” and we know from Table B.8 in Appendix B that the hit

rates are not equalized. Conversely, if α is close to one then the payoff π (α) will closely

replicate the variable “arrests,” and we know from Table 3 that hit rates are not equalized

either. We have performed a search for the threshold value α that equalizes the arrest rates

on π (α) across races (analysis not reported). This threshold value α turns out to be around

0.8.42 This means that the observed police behavior is consistent with that of a police force

which is unbiased and uses an α ≈ 0.8. Also, the observed police behavior is consistent with

that of a police force which is not biased against African Americans and uses an α > 0.8.43

A value of 0.8 implies that the police values each arrest equal to about four summons. We

regard this “conversion rate” as normatively not unacceptable—although of course readers

are free to make their own judgments. If that rate of 4 to 1 is found normatively acceptable,

then we conclude that the police are behaving in a way that is observably equivalent to

one whose tastes are in line with the normatively correct values, that is, zero bias and a

normatively acceptable α∗ ≈ 0.8.

7 Conclusions

New York City’s “stop and frisk” program disproportionately impacts minorities. At the

same time, former New York City’s police commissioner William Bratton said: “Stop-and-

frisk is not something you can stop. It is an absolutely basic tool of American policing.”44

If “stop and frisk” cannot be stopped, then it becomes especially important to ensure that

this program is carried out in a racially unbiased way. To this end, we have argued that a

strong theoretical foundation is needed which can rigorously identify two distinct sources of

bias: bias at the level of the police officer making the stop decisions, and bias at the level

of the police chief allocating manpower across precincts. Previous research offered positive

42Tables B.10 and B.11 report the main results when the dependent variable is π (0.8) . By construction,the estimated coefficients on “African American” in columns 6 and 7 of Tables B.10 are not significantlydifferent from zero, which means that arrest rates are equalized.

43This should be expected: if α is close to one then we are back to the analysis in Section 5.44The Wall Street Journal, “The Real Cures for Gun Violence” by David Feith. January 19-20, 2013.

29

identification results regarding officer bias; this paper adds a new, and negative, identification

result for police chief bias.

Ten years of data from NYPD’s “stop and frisk program” are analyzed in light of this

theoretical framework. After controlling for precinct-level fixed effects, white pedestrians are

found to be slightly less likely than African-American pedestrians to be arrested conditional

on being stopped. We interpret this fact as evidence that the officers on average are choosing

whom to stop in a manner consistent with no bias against African Americans, because Whites

are being stopped despite being a “less productive stop” for a police officer.

An analysis of the frisk decision reveals that, after controlling for precinct-level fixed effects,

African-American pedestrians are less likely than white pedestrians to be arrested conditional

on being frisked. We interpret this evidence as suggestive of bias against African Americans

in the frisk decision, though further research is needed on this point.

An important caveat: our analysis is based on the assumption that the decision to arrest

(as opposed to the stop-frisk decision) is not tainted by police bias. We have tested this

assumption to the extent possible with the data at hand, and found no evidence pointing to

its rejection. However, we feel that this assumption deserves further scrutiny.

Our results cannot be interpreted as proving that the stop and frisk program is lawful. It

is possible that the program may be unlawful in other ways. For example, the program’s

searches might not always arise from a reasonable suspicion.

30

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33

Appendices

A The Theory of Pedestrian and Officer Behavior, and

a Test for Officer Bias

Condition the analysis to precinct i, so that all variables in this section are precinct-specific.

We want to allow for officer heterogeneity within the district, and at the same time we

want to allow for additions (or subtractions) to the mass of police officers allocated to the

precinct. This raises the question of how the differential officers should affect the pre-

existing distribution of officer characteristics within the precinct. For simplicity, we assume

that officers are blank slates, and that they take on their characteristics (possible bias, cost

of searching, etc.) by drawing from a precinct-specific distribution. This modelling device

avoids the need for keeping track of changing officer characteristics in a precinct as the

precinct’s manpower is changed.

Let r denote the race of the pedestrian, which is assumed to be observable by the police.

Without loss of generality, assume that there are pedestrians of two races, either African

American (A) or white (W ). Other characteristics that are costlessly observable by the

police are represented by the number c ∈ {1, . . . , C}. These characteristics might represent

such things as the age or gender of the pedestrian. From the police viewpoint, a pedestrian

is characterized by two variables, r and c. Let N r,c denote the number of pedestrians belong

to group (r, c).

We assume that the police can distinguish between pedestrian groups (r, c), but cannot

detect pedestrian heterogeneity within (r, c) groups. Two sources of unobserved pedestrian

heterogeneity within groups are the values to an individual of committing a crime and the

costs of being detected. Let v represent the value of committing a crime. If the crime is

detected, the payoff to the pedestrian is v − j, where j captures the cost of being detected.

We allow v and j to vary across individuals within a (r, c) group and denote the joint

conditional distribution of v and j by cdf Fr,c (v, j) .

34

A pedestrian in group (r, c) makes a binary decision: commit a crime or not. Just as

pedestrians may differ in their costs and benefits, we allow police officers to be heterogeneous

in three respects: their search capacity, their per-search cost, and their racial bias. We assume

that there is a mass P of police officers, which after being assigned to the precinct, draw a

type p from a uniform distribution on [0, 1]. Each police officer p is endowed with a search

capacity of Sp and a per-search cost tp. If a search does not yield any evidence of crime, then

we term the search unsuccessful and assume that the police officer incurred the cost of search

without any benefit. We introduce the potential for police bias by allowing the benefit that

the police derives from a successful search to depend on the race of the pedestrian. Suppose

the benefit to a police officer p of finding a criminal of race W is yWp and the benefit of

finding criminal of race A is yAp = yWp +B (p) . We say that police are biased against African

American pedestrians if B (p) > 0 for all p, against whites if B (p) < 0 for all p, and unbiased

if B (p) = 0 for all p. If no search is conducted, there is a zero payoff. As described, this setup

accommodates police heterogeneity in intensity of bias. However, we rule out environments

in which B (p) changes sign as p varies, i.e., where some policemen are biased against whites

and some are biased against African Americans. Below, we propose a test for inferring the

sign of B (p).

A member of group (r, c) with given v, j, who commits a crime and expects σ members of

his group to be searched receives an expected payoff

ur,c (v, j, σ) = v − j ·σ

N r,c.

When this payoff exceeds zero, the individual will choose to commit a crime. Let Kr,c (v, j, σ)

be an indicator function that equals 1 if the individual chooses to commit a crime. The

fraction of pedestrians within each group (r, c) who commit a crime is given by

Kr,c (σ) =

∫

Kr,c (v, j, σ) dFr,c (v, j) .

The function Kr,c (σ) summarizes the crime rate in group (r, c) when the police search that

group with intensity σ. One can think of this function as a response function or as the supply

of crime.

35

Denote by Sp (r, c) the number of searches that officer p decides to devotes to group (r, c).

The total number of searches of members of group (r, c) is obtained by aggregating the

behavior of all police officers:

S (P, r, c) = P

∫ 1

0

Sp (r, c) dp.

Officer p’s expected payoff is the sum of the expected payoffs of all his searches, given by

∑

r,c

Sp (r, c)[

yrp ·Kr,c (S (P, r, c))− tp

]

, (3)

which depends on the officers perceived benefit from apprehending someone of race r (yrp) as

well as the officer’s costs of search (tp).

Persico and Todd (2006) show that a Nash equilibrium of this game exists and is generically

unique. Let [S∗ (P, r, c)]r,c be a vector denoting the search intensities at the Nash equilibrium.

Suppose groups (r, c) and (r′, c′) are searched in equilibrium. Then, there must be a p and

a p′ such that

yrpKr,c (S∗ (P, r, c))− tp ≥ yr

′

p Kr′,c′ (S∗ (P, r′, c′))− tp,

yrp′Kr,c (S∗ (P, r, c))− tp′ ≤ yr

′

p′Kr′,c′ (S∗ (P, r′, c′))− tp′ .

If r = r′, or if the police are unbiased then yrp = yr′

p for all p’s, and so the two inequalities

can only be simultaneously satisfied if

Kr,c (S∗ (P, r, c)) = Kr′,c′ (S∗ (P, r′, c′)) . (4)

If the police are biased against race r then yrp′ > yr′

p′ , and so the second inequality can only

be satisfied if the crime rates are such that

Kr,c (S∗ (P, r, c)) < Kr′,c′ (S∗ (P, r′, c′)) .

36

Note that in our model the hit rate, i.e., the likelihood that a search of group (r, c) yields

a find, coincides with that group’s crime rate Kr,c.Thus, the implications on the crime rate

translate into testable implications on the hit rates. This observation yields Theorem 1.

For use in Section 2 we now define the function

Kri (P ) = Kr,c (S∗ (P, r, c)) .

Note that the left hand side lacks a c argument, which makes sense because, by (4), we have

Kr,c (S∗ (P, r, c)) = Kr,c (S∗ (P, r, c′)) for all c, c′. By the same argument, it is proper to omit

reference to characteristics c in the model of Section 2.

We acknowledge that the test is based implicitly on the assumption that the only goal of

stops is to make arrests. To the extent that stops also serve other functions (e.g., deterrence),

and this function is not achieved through an arrest, then the test might show discrimination

where there is none.

37

B Extra Tables and Figures

Table B.1: Arrest Made Adding Hispanics

Model OLS OLS OLS FE FE FE FE(1) (2) (3) (4) (5) (6) (7)

African American -0.420*** -0.436*** -0.436 0.279*** 0.247*** 0.247 0.235(0.037) (0.037) (0.469) (0.043) (0.043) (0.187) (0.185)

Hispanic -0.119*** -0.149*** -0.149 -0.004 -0.029 -0.029 -0.000(0.039) (0.039) (0.344) (0.043) (0.043) (0.164) (0.161)

Constant 6.140***(0.034)

Mean outcome 5.86%Fraction of African American 56.1%Fraction of Hispanic 33.2%P-value of H0 : ui = 0 0.001 0.001 0.001 0.001Number of precincts 76 76 76 76Observations 4,413,566 4,413,566 4,413,566 4,413,566 4,413,566 4,413,566 4,413,566Cluster SE no no yes no no yes yesTime FE no yes yes no yes yes yesPrecincts FE no no no yes yes yes yesTime FE · Precincts FE no no no no no no yes

Notes. Estimates are on 76 precincts. The dependent variable is the probability of being arrested conditional onbeing stopped in New York City (in %). African American (Hispanic) is an indicator variable for African American(Hispanic) pedestrian. To control for possible time trend in the dependent variable and precincts specific characteristics,when denoted with “yes”, regressions additionally include year fixed effects (9 dummies) and precincts fixed effects (75dummies). In Column 7, we include interactions between year fixed effects (9 dummies) and precincts fixed effects (75dummies). Columns 3, 5-7, shows show clustered standard errors at the precinct level. P-value of H0 : ui = 0 is thep-value for the joint test of all the precincts fixed effects equal to zero. Significance at the 10% (*), at the 5% (**), andat the 1% (***).Source. Statistics for the City of New York, Years 2003-2012.

38

Table B.2: Arrest Made, Controlling for the Suspect’s Recorded Type of CrimeAdding Hispanics

Model OLS FE FE(1) (2) (3)

African American -0.582 0.138 0.140(0.424) (0.196) (0.194)

Hispanic -0.095 0.046 0.069(0.322) (0.172) (0.169)

Mean outcome 5.84%Fraction of African American pedestrians 56.4%Fraction of Hispanic pedestrians 33.1%P-value of H0 : ui = 0 0.001 0.001Number of precincts 76 76Observations 3,733,833 3,733,833 3,733,833Cluster SE yes yes yesTime FE yes yes yesPrecincts FE no yes yesCrime FE yes yes yesTime FE · Precincts FE no no yes

Notes. Estimates are on 76 precincts. The dependent variable is the probabilityof being arrested conditional on being stopped in New York City (in %). AfricanAmerican (Hispanic) is an indicator variable for African American (Hispanic)pedestrian. All the regressions include 13 indicators of the suspect’s recordedtype of crime representing 95% of the crimes (as recorded by the officer onForm UF-250). To control for possible time trend in the dependent variableand precincts specific characteristics, when denoted with “yes”, regressions ad-ditionally include year fixed effects (9 dummies) and precincts fixed effects (75dummies). In Column 3, we include interactions between year fixed effects (9dummies) and precincts fixed effects (75 dummies). Standard errors are clusteredat the precinct level. P-value of H0 : ui = 0 is the p-value for the joint test of allthe precincts fixed effects equal to zero. Significance at the 10% (*), at the 5%(**), and at the 1% (***).Source. Statistics for the City of New York, Years 2003-2012.

39

Table B.3: Arrest Made, Controlling for the Suspect’s Recorded Type of Crime

Model OLS FE FE(1) (2) (3)

African American -0.551 0.233 0.225(0.418) (0.217) (0.214)

Mean outcome 5.76%Fraction of African American pedestrians 84%P-value of H0 : ui = 0 0.001 0.001Number of precincts 76 76Observations 2,496,267 2,496,267 2,496,267Cluster SE yes yes yesTime FE yes yes yesPrecincts FE no yes yesCrime FE yes yes yesTime FE · Precincts FE no no yes

Notes. Estimates are on 76 precincts. The dependent variable is the probabilityof being arrested conditional on being stopped in New York City (in %). AfricanAmerican is an indicator variable coding the pedestrian’s race. All the regressionsinclude 13 indicators of the suspect’s recorded type of crime representing 95% ofthe crimes (as recorded by the officer on Form UF-250). To control for possibletime trend in the dependent variable and precincts specific characteristics, whendenoted with “yes”, regressions additionally include year fixed effects (9 dummies)and precincts fixed effects (75 dummies). In Column 3, we include interactionsbetween year fixed effects (9 dummies) and precincts fixed effects (75 dummies).Standard errors are clustered at the precinct level. P-value of H0 : ui = 0 is thep-value for the joint test of all the precincts fixed effects equal to zero. Significanceat the 10% (*), at the 5% (**), and at the 1% (***).Source. Statistics for the City of New York, Years 2003-2012.

40

Table B.4: Reasons for Arrest

Sample All Arrests African American White

(1) (2) (3)

Possession of marihuana 11 11 10

Trespass 9.4 10 6.2

Possession of controlled substance 8.3 7.6 12

Possession of weapon 7.7 7.9 6.9

Assault 4.5 4.2 6.1

Robbery 4.3 4.7 2.2

Larceny 3.9 3.7 4.6

Burglary 3.3 3.4 2.9

Possession of stolen property 1.2 1.1 1.5

Possession of a forged instrument .71 .74 .56

Menacing .64 .61 .75

Other 46 46 47Notes. Sample of 170, 595 arrests in New York City. Column 1 reports the sample mean in %. Column 2,3 sample means forAfrican Americans and Whites.Source. Statistics for the City of New York, Years 2003-2012.

41

Table B.5: Frisk Made, with the Suspect of Weapons PossessionModel OLS OLS OLS FE FE FE FE

(1) (2) (3) (4) (5) (6) (7)African American 4.900*** 4.937*** 4.938*** 2.972*** 2.996*** 2.996* 2.900*

(0.164) (0.164) (1.265) (0.184) (0.184) (1.643) (1.526)

Constant 83.058***(0.158)

Mean outcome 87.64%Fraction of African American 93.5%P-value of H0 : ui = 0 0.001 0.001 0.001 0.001Number of precincts 76 76 76 76Observations 663,813 663,813 663,812 663,812 663,812 663,812 663,812

Cluster SE no no yes no no yes yesTime FE no yes yes no yes yes yesPrecincts FE no no no yes yes yes yesTime FE · Precincts FE no no no no no no yes

Notes. Estimates are on 76 precincts. The dependent variable is the probability of being frisked in thesub-sample of stops with the suspect of weapons possession in New York City (in %). African Americanis an indicator variable coding the pedestrian’s race. To control for possible time trend in the dependentvariable and precincts specific characteristics, when denoted with “yes”, regressions additionally include yearfixed effects (9 dummies) and precincts fixed effects (75 dummies). In Column 7, we include interactionsbetween year fixed effects (9 dummies) and precincts fixed effects (75 dummies). Columns 3, 5-7, showsshow clustered standard errors at the precinct level. P-value of H0 : ui = 0 is the p-value for the joint testof all the precincts fixed effects equal to zero. Significance at the 10% (*), at the 5% (**), and at the 1%(***).Source. Statistics for the City of New York, Years 2003-2012.

42

Table B.6: Arrest for Weapons Possession Made, with the Suspect of WeaponsPossession and Frisked

Model OLS OLS OLS FE FE FE FE(1) (2) (3) (4) (5) (6) (7)

African American -2.027*** -2.023*** -2.023*** -1.259*** -1.263*** -1.263*** -1.254***(0.069) (0.069) (0.218) (0.079) (0.079) (0.218) (0.215)

Constant 2.619***(0.206)

Mean outcome 1.640%Fraction of African American 93.8%P-value of H0 : ui = 0 0.001 0.001 0.001 0.001Number of precincts 76 76 76 76Observations 581,763 581,763 581,763 581,763 581,763 581,763 581,763

Cluster SE no no yes no no yes yesTime FE no yes yes no yes yes yesPrecincts FE no no no yes yes yes yesTime FE · Precincts FE no no no no no no yes

Notes. Estimates are on 76 precincts. The dependent variable is the probability of arrest for weapons possession,conditional on being stopped with the suspect of weapons possession, in the sub-sample of stops with frisks in NewYork City (in %). African American is an indicator variable coding the pedestrian’s race. To control for possibletime trend in the dependent variable and precincts specific characteristics, when denoted with “yes”, regressionsadditionally include year fixed effects (9 dummies) and precincts fixed effects (75 dummies). In Column 7, weinclude interactions between year fixed effects (9 dummies) and precincts fixed effects (75 dummies). Columns3, 5-7, shows show clustered standard errors at the precinct level. P-value of H0 : ui = 0 is the p-value for thejoint test of all the precincts fixed effects equal to zero. Significance at the 10% (*), at the 5% (**), and at the1% (***).Source. Statistics for the City of New York, Years 2003-2012.

43

Table B.7: Arrest Made, with the Suspect of Weapons Possession and FriskedModel OLS OLS OLS FE FE FE FE

(1) (2) (3) (4) (5) (6) (7)African American -3.852*** -3.844*** -3.844*** -2.343*** -2.352*** -2.352*** -2.291***

(0.114) (0.114) (0.484) (0.130) (0.130) (0.459) (0.450)

Constant 6.728***(0.340)

Mean outcome 4.626%Fraction of African American 93.8%P-value of H0 : ui = 0 0.001 0.001 0.001 0.001Number of precincts 76 76 76 76Observations 581,763 581,763 581,763 581,763 581,763 581,763 581,763

Cluster SE no no yes no no yes yesTime FE no yes yes no yes yes yesPrecincts FE no no no yes yes yes yesTime FE · Precincts FE no no no no no no yes

Notes. Estimates are on 76 precincts. The dependent variable is the probability of arrest conditional on beingstopped with the suspect of weapons possession, in the sub-sample of stops with frisks in New York City (in %).African American is an indicator variable coding the pedestrian’s race. To control for possible time trend inthe dependent variable and precincts specific characteristics, when denoted with “yes”, regressions additionallyinclude year fixed effects (9 dummies) and precincts fixed effects (75 dummies). In Column 7, we includeinteractions between year fixed effects (9 dummies) and precincts fixed effects (75 dummies). Columns 3, 5-7,shows show clustered standard errors at the precinct level. P-value of H0 : ui = 0 is the p-value for the jointtest of all the precincts fixed effects equal to zero. Significance at the 10% (*), at the 5% (**), and at the 1%(***).Source. Statistics for the City of New York, Years 2003-2012.

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Table B.8: Summons Issued

Model OLS OLS OLS FE FE FE FE(1) (2) (3) (4) (5) (6) (7)

African American 0.070* 0.095** 0.095 -1.753*** -1.736*** -1.736*** -1.721***(0.038) (0.038) (0.360) (0.047) (0.047) (0.295) (0.276)

Constant 6.122***(0.035)

Mean outcome 6.18%Fraction of African American 84%P-value of H0 : ui = 0 0.001 0.001 0.001 0.001Number of precincts 76 76 76 76Observations 2,947,865 2,947,865 2,947,865 2,947,865 2,947,865 2,947,865 2,947,865Cluster SE no no yes no no yes yesTime FE no yes yes no yes yes yesPrecincts FE no no no yes yes yes yesTime FE · Precincts FE no no no no no no yes

Notes. Estimates are on 76 precincts. The dependent variable is the probability of a summons being issued conditionalon being stopped in New York City (in %). African American is an indicator variable coding the pedestrian’s race. Tocontrol for possible time trend in the dependent variable and precincts specific characteristics, when denoted with “yes”,regressions additionally include year fixed effects (9 dummies) and precincts fixed effects (75 dummies). In Column 7,we include interactions between year fixed effects (9 dummies) and precincts fixed effects (75 dummies). Columns 3, 5-7,shows show clustered standard errors at the precinct level. P-value of H0 : ui = 0 is the p-value for the joint test of allthe precincts fixed effects equal to zero. Significance at the 10% (*), at the 5% (**), and at the 1% (***).Source. Statistics for the City of New York, Years 2003-2012.

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Table B.9: Summons Issued, Controlling for the Suspect’s Recorded Type ofCrime

Model OLS FE FE(1) (2) (3)

African American -0.254 -1.464*** -1.487***(0.311) (0.293) (0.276)

Mean outcome 6.13%Fraction of African American pedestrians 84%P-value of H0 : ui = 0 0.001 0.001Number of precincts 76 76Observations 2,496,267 2,496,267 2,496,267Cluster SE yes yes yesTime FE yes yes yesPrecincts FE no yes yesCrime FE yes yes yesTime FE · Precincts FE no no yes

Notes. Estimates are on 76 precincts. The dependent variable is the probabilityof a summons being issued conditional on being stopped in New York City (in%). African American is an indicator variable coding the pedestrian’s race. Allthe regressions include 13 indicators of the suspect’s recorded type of crimerepresenting 95% of the crimes (as recorded by the officer on Form UF-250). Tocontrol for possible time trend in the dependent variable and precincts specificcharacteristics, when denoted with “yes”, regressions additionally include yearfixed effects (9 dummies) and precincts fixed effects (75 dummies). In Column3, we include interactions between year fixed effects (9 dummies) and precinctsfixed effects (75 dummies). Standard errors are clustered at the precinct level.P-value of H0 : ui = 0 is the p-value for the joint test of all the precincts fixedeffects equal to zero. Significance at the 10% (*), at the 5% (**), and at the 1%(***).

46

Table B.10: Arrest Made and Summons Issued (Weighted)

Model OLS OLS OLS FE FE FE FE(1) (2) (3) (4) (5) (6) (7)

African American -0.322*** -0.331*** -0.331 -0.048 -0.063* -0.063 -0.072(0.030) (0.030) (0.379) (0.037) (0.037) (0.177) (0.171)

Constant 6.136***(0.028)

Mean outcome 5.86%Fraction of African American 84%P-value of H0 : ui = 0 0.001 0.001 0.001 0.001Number of precincts 76 76 76 76Observations 2,947,867 2,947,867 2,947,865 2,947,865 2,947,865 2,947,865 2,947,865Cluster SE no no yes no no yes yesTime FE no yes yes no yes yes yesPrecincts FE no no no yes yes yes yesTime FE · Precincts FE no no no no no no yes

Notes. Estimates are on 76 precincts. The dependent variable is (π(α) = α · Iarrest + (1− α) · Isummons) the weightedsum of the probability of being arrested and the probability of a summons being issued conditional on being stoppedin New York City (in %). The weights (α, 1 − α) are .8 and .2. African American is an indicator variable coding thepedestrian’s race. To control for possible time trend in the dependent variable and precincts specific characteristics,when denoted with “yes”, regressions additionally include year fixed effects (9 dummies) and precincts fixed effects(75 dummies). In Column 7, we include interactions between year fixed effects (9 dummies) and precincts fixed effects(75 dummies). Columns 3, 5-7, shows show clustered standard errors at the precinct level. P-value of H0 : ui = 0is the p-value for the joint test of all the precincts fixed effects equal to zero. Significance at the 10% (*), at the 5%(**), and at the 1% (***).Source. Statistics for the City of New York, Years 2003-2012.

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Table B.11: Arrest Made and Summons Issued, Controlling for the Type ofCrime (Weighted)

Model OLS FE FE(1) (2) (3)

African American -0.492 -0.107 -0.118(0.333) (0.170) (0.166)

Mean outcome 5.86%Fraction of African American pedestrians 84%P-value of H0 : ui = 0 0.001 0.001Number of precincts 76 76Observations 2,496,267 2,496,267 2,496,267Cluster SE yes yes yesTime FE yes yes yesPrecincts FE no yes yesCrime FE yes yes yesTime FE · Precincts FE no no yes

Notes. Estimates are on 76 precincts. The dependent variable is (π(α) =α · Iarrest + (1 − α) · Isummons) the weighted sum of the probability of beingarrested and the probability of a summons being issued conditional on be-ing stopped in New York City (in %). The weights (α, 1 − α) are .8 and .2.African American is an indicator variable coding the pedestrian’s race. Allthe regressions include 13 indicators of the suspect’s recorded type of crimerepresenting 95% of the crimes (as recorded by the officer on Form UF-250).To control for possible time trend in the dependent variable and precinctsspecific characteristics, when denoted with “yes”, regressions additionally in-clude year fixed effects (9 dummies) and precincts fixed effects (75 dummies).In Column 3, we include interactions between year fixed effects (9 dummies)and precincts fixed effects (75 dummies). Standard errors are clustered atthe precinct level. P-value of H0 : ui = 0 is the p-value for the joint test ofall the precincts fixed effects equal to zero. Significance at the 10% (*), atthe 5% (**), and at the 1% (***).Source. Statistics for the City of New York, Years 2003-2012.

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C Replication with “mandates reports” sample

To identify mandated reports we followed the definition at pg. XV of the New York Attorney

General report on Stop and Frisk.45 These so-called ‘mandated reports’ are stops that involve

physical force, a frisk, an arrest, or the pedestrian’s refusal to provide identification. The

NYPD data, however, has a limitation: the outcome “refused to identify” is not recorded in

the data. We proxy for it using the field “evasive response to questioning.”

Table C.1: Descriptive Statistics, Mandated Stops

Mean sd nOutcomesArrest made .10 .30 1,681,600Race of the pedestrianAfrican American .87 .34 1,681,600Suspect’s recorded type of crimePossession of a Weapon .4 .49 1,480,728Robbery .19 .39 1,480,728Criminal Trespass .056 .23 1,480,728Grand Larceny Auto .065 .25 1,480,728Burglary .066 .25 1,480,728Grand Larceny .037 .19 1,480,728Illegal Possession of Substances .031 .17 1,480,728Assault .032 .18 1,480,728Marihuana .033 .18 1,480,728Illegal Sales of Substances .023 .15 1,480,728Petit Larceny .017 .13 1,480,728Mischief .0085 .092 1,480,728Graffiti .0077 .088 1,480,728Other Crimes .032 .18 1,480,728

Notes. African American is an indicator variable coding thepedestrian’s race. Crime details are 13 indicators of the sus-pect’s recorded type of crime represent 95% of the crimesrecorded in the sample. Years 2003-2005 have missing valuesin the variable Crime details.Source. Statistics for the City of New York, Years 2003-2012.

45Refer to http://www.oag.state.ny.us/sites/default/files/pdfs/bureaus/civil rights/stp frsk.pdf

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Table C.2: Arrest Made, Mandated Stops

Model OLS OLS OLS FE FE FE FE(1) (2) (3) (4) (5) (6) (7)

African American -3.629*** -3.645*** -3.645*** -1.625*** -1.627*** -1.627*** -1.668***(0.069) (0.069) (0.835) (0.084) (0.084) (0.554) (0.510)

Constant 13.30448***(0.065)

Mean outcome 10.14%Fraction of African American 87%P-value of H0 : ui = 0 0.001 0.001 0.001 0.001Number of precincts 76 76 76 76Observations 1,681,600 1,681,600 1,681,600 1,681,600 1,681,600 1,681,600 1,681,600Cluster SE no no yes no no yes yesTime FE no yes yes no yes yes yesPrecincts FE no no no yes yes yes yesTime FE · Precincts FE no no no no no no yes

Notes. Estimates are on 76 precincts. The dependent variable is the probability of being arrested conditional on beingstopped in New York City (in %). African American is an indicator variable coding the pedestrian’s race. To control forpossible time trend in the dependent variable and precincts specific characteristics, when denoted with “yes”, regressionsadditionally include year fixed effects (9 dummies) and precincts fixed effects (75 dummies). In Column 7, we includeinteractions between year fixed effects (9 dummies) and precincts fixed effects (75 dummies). Columns 3, 5-7, shows showclustered standard errors at the precinct level. P-value of H0 : ui = 0 is the p-value for the joint test of all the precinctsfixed effects equal to zero. Significance at the 10% (*), at the 5% (**), and at the 1% (***).Source. Statistics for the City of New York, Years 2003-2012.

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Table C.3: Arrest Made, Controlling for the Suspect’s Recorded Type of Crime,Mandated Stops

Model OLS FE FE(1) (2) (3)

African American -1.529** -0.524 -0.543(0.713) (0.427) (0.411)

Mean outcome 9.705%Fraction of African American pedestrians 87%P-value of H0 : ui = 0 0.001 0.001Number of precincts 76 76Observations 1,480,728 1,480,728 1,480,728Cluster SE yes yes yesTime FE yes yes yesPrecincts FE no yes yesCrime FE yes yes yesTime FE · Precincts FE no no yes

Notes. Estimates are on 76 precincts. The dependent variable is the probabilityof being arrested conditional on being stopped in New York City (in %). AfricanAmerican is an indicator variable coding the pedestrian’s race. All the regressionsinclude 13 indicators of the suspect’s recorded type of crime representing 95% ofthe crimes (as recorded by the officer on Form UF-250). To control for possibletime trend in the dependent variable and precincts specific characteristics, whendenoted with “yes”, regressions additionally include year fixed effects (9 dummies)and precincts fixed effects (75 dummies). In Column 3, we include interactionsbetween year fixed effects (9 dummies) and precincts fixed effects (75 dummies).Standard errors are clustered at the precinct level. P-value of H0 : ui = 0 is thep-value for the joint test of all the precincts fixed effects equal to zero. Significanceat the 10% (*), at the 5% (**), and at the 1% (***).Source. Statistics for the City of New York, Years 2003-2012.

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Table C.4: Correlates of Relative Police Pressure in New York City, MandatedStops

Model OLS OLS OLSSample Panel Panel Panel

(1) (2) (3)Fraction of African American -0.273*** -0.061 -0.095

(0.088) (0.072) (0.063)Income 0.469*** 0.435***

(0.141) (0.135)Constant 28.885*** -5.201 -13.098

(4.703) (8.154) (30.915)

Relative police pressure (average) 21.58Fraction of African Americans (in %) in the average precinct 26.78Number of precincts 75 75 75Observations 750 750 750Adj. R2 0.0793 0.267 0.470Precinct Controls no no yesTime FE no yes yes

Notes. Estimates are on 75 precincts. The dependent variable is (relative) police pressure

(ArrestsofAfricanAmericansAfricanAmericanpopulation

ArrestsofWhitesWhitepopulation

) in New York City. Fraction of African American is the percentage of

the population that is African American in the precinct in 2010. Income is the inflation adjustedmedian income in the precinct in 2010. Column 3 also includes the difference between M. Bloombergand the first running opponent M. Green, or F. Ferrer, or B. Thompson vote share in the 2001, 2005,2009 elections, respectively. Missing years are computed using moving averages; the percentage ofthe population that is African American in the precinct in 2010; the inflation adjusted median in-come, 2010 precinct average; the median age, 2010 precinct average; the precinct average percentageof the population that is female in 2010; the precinct average percentage of the population aged15-24 with a college degree in 2010; the number of annual crimes (murders, rapes, robberies, fel.assaults, burglaries, grand larcenies, grand larceny autos) in each precinct divided by the precinctpopulation in 2010 (in 1,000 habitants) for the years 1998, 2001, 2012; the number of annual graf-fiti in each precinct in 2011 divided by the precinct population in 2010 (in 1,000 habitants); thetotal number of annual civic initiatives (education, emergency preparedness, environment, helpingneighbours in need, strengthening communities) in each precinct, in 2011 divided by the precinctpopulation in 2010 (in 1,000 habitants); and an indicator for African American commanding officers.All variables are described in Appendix C.To control for possible time trend in the dependent variable and precincts specific characteristics,when denoted with “yes” regressions additionally include year fixed effects (9 dummies). Standarderrors are clustered at the precinct level. Significance at the 10% (*), at the 5% (**), and at the 1%(***).Source. Statistics for the City of New York, Years 2003-2012. Resident population from the 2010Census data.

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D Variables, Descriptions, and Sources

Variable Description SourceAfrican American Indicator variable coding whether the pedestrian is African American NYPD, Stop-and-Frisk

Database

Hispanic Indicator variable coding whether the pedestrian is Hispanic NYPD, Stop-and-FriskDatabase

Relative policepressure

ArrestsofAfricanAmericansAfricanAmericanpopulation

ArrestsofWhitesWhitepopulation

in each of the New York City police precinct NYPD Stop-and-FriskDatabase

Margin ofBloomberg vic-tory

Difference between M. Bloomberg and the first running opponent M. Green, or F. Ferrer, or B. Thomp-son vote share in the 2001, 2005, 2009 elections, respectively. Missing years are computed using movingaverages. Original data: Electoral district data (2001, 2005, 2005 districts) matched with police precinctsusing the Stata routine gpsmap.ado

NYC Board of Elections

Fraction ofAfrican American

is the percentage of the population that is African American in the precinct in 2010. Original data: ZIPCode level data matched with police precincts using the Stata routine gpsmap.ado

U.S. Census Bureau, 2011

Income Inflation adjusted median income, 2010 precinct average. Original data: ZIP Code level data matched withpolice precincts using the Stata routine gpsmap.ado

American Community Sur-vey (5-year), U.S. CensusBureau

Age Median age, 2010 precinct average. Original data: ZIP Code level data matched with police precincts usingthe Stata routine gpsmap.ado

American Community Sur-vey (5-year), U.S. CensusBureau

Fraction of female is the precinct average percentage of the population that is female in 2010. Original data: ZIP Code leveldata matched with police precincts using the Stata routine gpsmap.ado

American Community Sur-vey (5-year), U.S. CensusBureau

Fraction of col-lege degree

is the precinct average percentage of the population aged 15-24 with a college degree in 2010. Originaldata: ZIP Code level data matched with police precincts using the Stata routine gpsmap.ado

American Community Sur-vey (5-year), U.S. CensusBureau

Serious crime Number of annual crimes (murders, rapes, robberies, fel. assaults, burglaries, grand larcenies, grand larcenyautos) in each precinct divided by the precinct population in 2010 (in 1,000 habitants) for the years 1998,2001, 2012. Missing years are computed using moving averages. Original data: Data matched with policeprecincts by the NYPD

NYPD, crime statistics

Graffiti Number of annual graffiti in each precinct in 2011 divided by the precinct population in 2010 (in 1,000habitants). Original data: Data matched with police precincts by the NY Police Department

Graffiti Locations, NYCOpen Data

Social capital Number of annual civic initiatives (education, emergency preparedness, environment, helping neighbors inneed, strengthening communities) in each precinct, in 2011 divided by the precinct population in 2010 (in1,000 habitants). Original data: Latitude-Longitude geo-coded data matched with police precincts usingthe Stata routine gpsmap.ado

NYC Service VolunteerOpportunities, NYC OpenData

African Americancommander

Indicator for African American commanding officers. Original data: NY police borough matched withpolice precincts

NYC Journal articles

53